Here's a simple solution. The referee has the option to, if in doubt, consult someone with a video replay to determine a situation. He already has, and uses, the option to consult the line men, so it is not obvious to me why he shouldn't be able to consult someone who can watch a replay.

Another thing that for the life of me I cannot understand hasn't been implemented: A chip in the ball to determine off sides and whether the ball has crossed the goal or side lines.